Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach

Appraisal of the Fragments-In-Fragments Method for the Energetics of Individual Hydrogen Bonds in Molecular Crystals

We report a direct application of the molecular tailoring approach-based (MTA-based) method to calculate the individual hydrogen bond (HB) energy in molecular crystal. For this purpose, molecular crystals of nitromalonamide (NMA) and salicylic acid (SA) were taken as test cases. Notably, doing a correlated computation using a large molecular crystal structure is difficult. Among 15 density functional theory functionals, the B3LYP provides accurate estimates of HB energies closed to the CCSD(T) ones using the 6-311 + G(d,p) basis set for all atoms. The direct application of the MTA-based method to these crystal structures is although straightforward. For instance, the calculated energy suggests that three intramolecular HBs in NMA crystal are of stronger strength (7.3-17.0 kcal/mol) than the intermolecular ones (2.7-4.0 kcal/mol). On the other hand, intermolecular HB in SA crystal is moderately stronger (9.9 kcal/mol) than intramolecular one (8.1 kcal/mol). However, these energy calculations by the MTA-based method are very expensive. For instance, the time needed to evaluate the energy of all seven HBs in NMA crystal (having molecules within maximum of 15 unit cells) is 122,681 min (~2.7 months). In view of this, we assessed our recently proposed linear-scaling Fragments-in-Fragments (Frags-in-Frags) method for estimating the single-point energies of parent molecular crystal and fragments of the MTA-based method. It has been found that the estimated HB energies by the Frags-in-Frags method are in excellent linear agreement with their MTA-based counterparts (R2 = 0.9993). Furthermore, root mean square deviation is 0.12 kcal/mol. Mean and maximum absolute errors are 0.10 and 0.5 kcal/mol, respectively, and the standard deviation is 0.14 kcal/mol. Importantly, the Frags-in-Frags method is computationally efficient; it needs only 18,289 min (~12.7 days) for the estimation of energy of all HBs in NMA crystal and 3499 min (~2.4 days) for all HBs in SA crystal.

Molecular Tailoring Approach for the Direct Estimation of Individual Noncovalent Interaction Energies in Molecular Systems

The noncovalent interactions (NCIs) are omnipresent in chemistry, physics, and biology. The study of such interactions offers insights into various physicochemical phenomena. Some indirect approaches proposed in the literature for exploring the NCIs are briefly reviewed in Section 1 of this Perspective. These include: (i) Shift in the stretching frequency of an X-Y bond involved in X-Y···Z interaction. (ii) Topological analysis of molecular electron density. (iii) Empirical equations derived employing experimental and theoretical quantities. However, a direct method for estimating individual intramolecular/intermolecular interaction energies has been conspicuous by its absence from the literature. We have developed a molecular tailoring approach (MTA)-based method enabling a direct and reliable estimation of the energy of intra- as well as intermolecular interactions. This method offers a direct and reliable estimation of these interactions, in particular of the hydrogen bonds (HB) in molecules/weakly bound clusters along with the respective cooperativity contribution. In Section 2, the basis of our method is discussed, along with some illustrative examples. The application of this method to a variety of molecules and clusters, with a special emphasis on estimating the HB energy along with the energy of other NCIs is presented in Section 3. Section 4 discusses some computational strategies for applying our method to large molecular clusters. The last Section provides a summary and a discussion on future developments.

Hydrogen bond energy estimation (H-BEE) in large molecular clusters: A Python program for quantum chemical investigations

A procedure, derived from the fragmentation-based molecular tailoring approach (MTA), has been proposed and extensively applied by Deshmukh and Gadre for directly estimating the individual hydrogen bond (HB) energies and cooperativity contributions in molecular clusters. However, the manual fragmentation and high computational cost of correlated quantum chemical methods make the application of this method to large molecular clusters quite formidable. In this article, we report an in-house developed software for automated hydrogen bond energy estimation (H-BEE) in large molecular clusters. This user-friendly software is essentially written in Python and executed on a Linux platform with the Gaussian package at the backend. Two approximations to the MTA-based procedure, viz. the first spherical shell (SS1) and the Fragments-in-Fragments (Frags-in-Frags), enabling cost-effective, automated evaluation of HB energies and cooperativity contributions, are also implemented in this software. The software has been extensively tested on a variety of molecular clusters and is expected to be of immense use, especially in conjunction with correlated methods such as MP2, CCSD(T), and so forth.

Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.

Fragments-in-fragments method for efficient and reliable estimates of individual hydrogen bond energies in large molecular clusters

The knowledge of individual hydrogen bond (HB) strength in molecular clusters is indispensable to get insights into the bulk properties of condensed systems. Recently, we have developed the molecular tailoring approach based (MTA-based) method for the estimation of individual HB energy in molecular clusters. However, the direct use of this MTA-based method to large molecular clusters becomes progressively difficult with the increase in the size of a cluster. To overcome this caveat, herein, we propose the use of linear scaling method (such as the original MTA method) for the estimation of single-point (SP) energies of large-sized parent molecular cluster and their respective fragments. Because the fragments of the MTA-based method, for the estimation of HB energy, are further fragmented, this proposed strategy is called as Fragments-in-Fragments (Frags-in-Frags) method. The SP energies of fragments and parent cluster calculated by the Frags-in-Frags approach were utilized to estimate the individual HB energy. The estimated individual HB energies, in various molecular clusters, by Frags-in-Frags method are found to be in excellent linear agreement with their MTA-based counterparts (R²  = 0.9975 of 348 data points). The difference being less than 0.5 kcal/mol in most of the cases. Furthermore, RMSD is 0.43 kcal/mol, MAE is 0.33 kcal/mol, and the standard deviation is 0.44 kcal/mol. Importantly, the Frags-in-Frags method not only enables the reliable estimation of HB energy in large molecular clusters but also requires less computational time and can be possible even with off-the-shelf hardware.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Tracking the Amide I and αCOO- Terminal ν(C=O) Raman Bands in a Family of l-Glutamic Acid-Containing Peptide Fragments: A Raman and DFT Study

The E-hook of β-tubulin plays instrumental roles in cytoskeletal regulation and function. The last six C-terminal residues of the βII isotype, a peptide of amino acid sequence EGEDEA, extend from the microtubule surface and have eluded characterization with classic X-ray crystallographic techniques. The band position of the characteristic amide I vibration of small peptide fragments is heavily dependent on the length of the peptide chain, the extent of intramolecular hydrogen bonding, and the overall polarity of the fragment. The dependence of the E residue's amide I ν(C=O) and the αCOO- terminal ν(C=O) bands on the neighboring side chain, the length of the peptide fragment, and the extent of intramolecular hydrogen bonding in the structure are investigated here via the EGEDEA peptide. The hexapeptide is broken down into fragments increasing in size from dipeptides to hexapeptides, including EG, ED, EA, EGE, EDE, DEA, EGED, EDEA, EGEDE, GEDEA, and, finally, EGEDEA, which are investigated with experimental Raman spectroscopy and density functional theory (DFT) computations to model the zwitterionic crystalline solids (in vacuo). The molecular geometries and Boltzmann sum of the simulated Raman spectra for a set of energetic minima corresponding to each peptide fragment are computed with full geometry optimizations and corresponding harmonic vibrational frequency computations at the B3LYP/6-311++G(2df,2pd) level of theory. In absence of the crystal structure, geometry sampling is performed to approximate solid phase behavior. Natural bond order (NBO) analyses are performed on each energetic minimum to quantify the magnitude of the intramolecular hydrogen bonds. The extent of the intramolecular charge transfer is dependent on the overall polarity of the fragment considered, with larger and more polar fragments exhibiting the greatest extent of intramolecular charge transfer. A steady blue shift arises when considering the amide I band position moving linearly from ED to EDE to EDEA to GEDEA and, finally, to EGEDEA. However, little variation is observed in the αCOO- ν(C=O) band position in this family of fragments.

Partitioning of the Vibrational Free Energy

Vibrational energies are partitioned into the contributions of molecular parts called segments, for instance, residues in proteins. The fragment molecular orbital method is used to facilitate vibrational calculations of large systems at the DFTB and HF-3c levels. The vibrational analysis is combined with the partitioning of the electronic energy, yielding free-energy contributions of segments to the binding energy, pinpointing hot spots for drug discovery and other studies. The analysis is illustrated on two protein-ligand complexes in solution.

Molecular Tailoring Approach for the Estimation of Intramolecular Hydrogen Bond Energy

Hydrogen bonds (HBs) play a crucial role in many physicochemical and biological processes. Theoretical methods can reliably estimate the intermolecular HB energies. However, the methods for the quantification of intramolecular HB (IHB) energy available in the literature are mostly empirical or indirect and limited only to evaluating the energy of a single HB. During the past decade, the authors have developed a direct procedure for the IHB energy estimation based on the molecular tailoring approach (MTA), a fragmentation method. This MTA-based method can yield a reliable estimate of individual IHB energy in a system containing multiple H-bonds. After explaining and illustrating the methodology of MTA, we present its use for the IHB energy estimation in molecules and clusters. We also discuss the use of this method by other researchers as a standard, state-of-the-art method for estimating IHB energy as well as those of other noncovalent interactions.

Computational Methods for Biochemical Simulations Implemented in GAMESS

Computational methods for modeling biochemical processes implemented in GAMESS package are reviewed; in particular, quantum mechanics combined with molecular mechanics (QM/MM), semi-empirical, and fragmentation approaches. A detailed summary of capabilities is provided for the QM/MM implementation in QuanPol program and the fragment molecular orbital (FMO) method. Molecular modeling and visualization packages useful for biochemical simulations with GAMESS are described. GAMESS capabilities with corresponding references are tabulated for reader's convenience.

Partition Analysis for Density-Functional Tight-Binding

High-order charge transfer is incorporated into the fragment molecular orbital (FMO) method using a charge transfer state with fractional charges. This state is used for a partition analysis of properties based on segments that may be different from fragments in FMO. The partition analysis is also formulated for calculations without fragmentation. All development in this work is limited to density-functional tight-binding. The analysis is applied to a water cluster, crambin (PDB: 1CBN), and two complexes of Trp-cage (1L2Y) with ligands. The contributions of functional groups in ligands are obtained, providing useful information for drug discovery.

Geometry Optimization, Transition State Search, and Reaction Path Mapping Accomplished with the Fragment Molecular Orbital Method

Recent development of the fragment molecular orbital (FMO) method related to energy gradients, geometry optimization, transition state search, and chemical reaction mapping is summarized. The frozen domain formulation of FMO is introduced in detail, and the structure of related GAMESS input files for FMO is described.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Solvent Screening in Zwitterions Analyzed with the Fragment Molecular Orbital Method

Based on induced solvent charges, a new model of solvent screening is developed in the framework of the fragment molecular orbital combined with the polarizable continuum model. The developed model is applied to analyze interactions in a prototypical zwitterionic system, sodium chloride in water, and it is shown that the large underestimation of the interaction in the original solvent screening based on local charges is successfully corrected. The model is also applied to a complex of the Trp-cage (PDB: 1L2Y ) miniprotein with an anionic ligand, and the physical factors determined protein-ligand binding in solution are unraveled.

Understanding PIM-1 kinase inhibitor interactions with free energy simulation

The proviral integration site of the Moloney leukemia virus (PIM) family includes three homologous members. PIM-1 kinase is an important target in effective therapeutic interventions of lymphomas, prostate cancer and leukemia. In the current work, we performed free energy calculations to calculate the binding affinities of several inhibitors targeting this protein. The alchemical method with integration and perturbation-based estimators and the end-point methods were compared. The computational results indicated that the alchemical method can accurately predict the binding affinities, while the end-point methods give relatively unreliable predictions. Decomposing the free energy difference into enthalpic and entropic components with MBAR reweighting enabled us to investigate the detailed thermodynamic parameters with which the entropy-enthalpy compensation in this protein-ligand binding case is identified. We then studied the conformational ensemble, and the important protein-ligand interactions were identified. The current work sheds light on the understanding of the PIM-1-kinase-inhibitor interactions at the atomic level and will be useful in the further development of potential drugs.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.

Anharmonic Theoretical Vibrational Spectroscopy of Polypeptides

Because of the size of polypeptides and proteins, the quantum-chemical prediction of their vibrational spectra presents an exceptionally challenging task. Here, we address one of these challenges, namely, the inclusion of anharmonicities. By performing the expansion of the potential energy surface in localized-mode coordinates instead of the normal-mode coordinates, it becomes possible to calculate anharmonic vibrational spectra of polypeptides efficiently and reliably. We apply this approach to calculate the infrared, Raman, and Raman optical activity spectra of helical alanine polypeptides consisting of up to 20 amino acids. We find that while anharmonicities do not alter the band shapes, simple scaling procedures cannot account for the different shifts found for the individual bands. This closes an important gap in theoretical vibrational spectroscopy by making it possible to quantify the anharmonic contributions and opens the door to a first-principles calculation of multidimensional vibrational spectra.